You need to look to the specific aircraft type for an answer. Yes, many transport category aircraft use a two-axis autopilot. The B742, for example, uses a two-axis autopilot. The autopilot system controls the airplane it pitch and roll. An independent yaw damper system provides support on the vertical axis in yaw, by reducing sideslipping yaw that can become dutch roll.
During approach, when the airplane is configured to land, the yaw damper system also provides an elementary turn coordination feature. This occurs automatically with flap extension.
Most large airplanes, indeed most transport category aircraft, require very little rudder input for most of the flight; a characteristic of "jet" pilots is a tendency to be lazy with their feet. Feet are often flat on the floor with not much rudder input at all. The B742 is very stable and takes almost no rudder input, most of the time. The exception is an engine-out, but even then the rudder is so large that it is powerful, and it's possible to overcontrol if one gets too aggressive with the rudder. Throwing full rudder in also causes roll, and once the contrl wheel goes past 1.8 units of roll spoilers extend as well as ailerons deflecting, and both yaw and roll are affected again. It can be entertaining to watch someone overcontrol in one axis in a simulator, because it can quickly turn to a juggling act as each of the other axes goes haywire.
The short answer is that the rudder isn't needed much during normal flight operations. It's not moved much, either, except for engine-out situations or assymetrical thrust.